[1] Smirnov, S.N.: Realistic models of financial market and structural stability. J. Math. (2021). https://doi.org/10.1155/2021/6651324
[2] Schachermayer, W.: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math. Financ. 14(1), 19-48 (2004)
[3] Bayraktar, E., Zhang, Y., Zhou, Z.: A note on the fundamental theorem of asset pricing under model uncertainty. Risks 2(4), 425-433 (2014)
[4] Ostrovski, V.: Stability of no-arbitrage property under model uncertainty. Stat. Probab. Lett. 83, 89-92 (2013)
[5] Hou, Z., Obƚój, J.: Robust pricing-hedging dualities in continuous time. Finance Stoch. 22, 511-567 (2018)
[6] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: no arbitrage properties of the market. Autom. Remote. Control. 82, 172-187 (2021)
[7] Davis, M., Hobson, D.: The range of traded option prices. Math. Finance 17, 1-14 (2007)
[8] Acciaio, B., Beiglböck, M., Penkner, F., Schachermayer, W.: A model-free version of the fundamental theorem of asset pricing and the super-replication theorem. Math. Financ. 26, 233-251 (2013)
[9] Bouchard, B., Nutz, M.: Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab. 25, 823-859 (2015)
[10] Burzoni, M., Frittelli, M., Maggis, M.: Universal arbitrage aggregator in discrete-time markets under uncertainty. Finance Stoch. 20, 1-50 (2016)
[11] Burzoni, M., Frittelli, M., Maggis, M.: Model-free superhedging duality. Ann. Appl. Probab. 27, 1452-1477 (2017)
[12] Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., Obƚój, J.: Pointwise arbitrage pricing theory in discrete time. Math. Oper. Res. 44, 1034-1057 (2018)
[13] Kolokoltsov, V.N.: Nonexpansive maps and option pricing theory. Kybernetika 34, 713-724 (1998)
[14] Bernhard, P., Engwerda, J.C., Roorda, B., et al.: The Interval Market Model in Mathematical Finance: Game-Theoretic Methods. Springer, New York (2013)
[15] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: sensitivity of solutions of Bellman-Isaacs equations and numerical methods. Comput. Math. Model. 31, 384-401 (2020)
[16] Carassus, L., Obƚój, J., Wiesel, J.: The robust superreplication problem: a dynamic approach. SIAM J. Financ. Math. 10, 907-941 (2019)
[17] Carassus, L., Obƚój, J., Wiesel, J.: Erratum to “The Robust Superreplication Problem: A Dynamic Approach”. SIAM Journal on Financial Mathematics 13, 653-655 (2022)
[18] Smirnov, S.N.: Guaranteed deterministic approach to superhedging: the semicontinuity and continuity properties of solutions of the Bellman-Isaacs equations. Autom. Remote. Control. 82, 2024-2040 (2021)
[19] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: financial market model, trading constraints, and the Bellman-Isaacs equations. Autom. Remote. Control. 82, 722-743 (2021)
[20] Carassus, L., Vargiolu, T.: Super-replication price: It can be OK. ESAIM Proc. Surv. 65, 241-281 (2018)
[21] Smirnov, S.N.: Geometric criterion for a robust condition of no sure arbitrage with unlimited profit. Mosc. Univ. Comput. Math. Cybern. 44, 146-150 (2020)
[22] Jacod, J., Shiryaev, A.N.: Local martingales and the fundamental asset pricing theorems in the discrete-time case. Finance Stoch. 2, 259-273 (1998)
[23] Carassus, L., Lépinette, E.: Pricing without no-arbitrage condition in discrete time. J. Math. Anal. Appl. 505, 125441 (2022)
[24] Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
[25] Cherif, D., Lépinette, E.: No-arbitrage conditions and pricing from discrete-time to continuous-time strategies. Ann. Finance 19, 141-168 (2023)
[26] Gerhold, S., Krühner, P.: Dynamic trading under integer constraints. Finance Stoch. 2018(22), 919-957 (2018)
[27] Smirnov, S.N.: The guaranteed deterministic approach to superhedging: Lipschitz properties of solutions of the Bellman-Isaacs equations. In: Frontiers of Dynamics Games: Game Theory and Management, Birkhäuser, St. Petersburg. pp. 267-288 (2019)
[28] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: relation between “deterministic” and “stochastic” settings in the case of no trading constraints. Theory Probab. Appl. 67, 548-569 (2023)
[29] Smirnov, S.N.: Structural stability threshold for the condition of robust no deterministic sure arbitrage with unbounded profit. Mosc. Univ. Comput. Math. Cybern. 45, 34-44 (2021)
[30] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: structural stability and approximation. Comput. Math. Model. 32, 129-146 (2021)
[31] Goberna, M.A., González, E., Martínez-Legaz, J.E., Todorov, M.I.: Motzkin decomposition of closed convex sets. J. Math. Anal. Appl. 364, 209-221 (2010)
[32] Smirnov, S.N.: Guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium. Autom. Remote. Control. 83, 2019-2036 (2022)
[33] Smirnov, S.N.: A note on transition kernels for the most unfavourable mixed strategies of the market. J. Oper. Res. Soc, China (2023). https://doi.org/10.1007/s40305-023-00490-4
[34] Leichtweiß, K.: Konvexe Mengen. Springer-Verlag, Berlin Heidelberg (1979)
[35] Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis: Theory, Mathematics and Its Applications, vol. I. Springer, Berlin (1997)
[36] Smirnov, S.N.: A guaranteed deterministic approach to superhedging: a game equilibrium in the case of no trading constraints. J. Math. Sci. 248, 105-115 (2020)
[37] Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis A Hitchhiker’s Guide, 3rd edn. Springer-Verlag, Berlin (2006)
[38] Karlin, S.: Extreme points of vector functions. Proc. Am. Math. Soc. 4, 603-610 (1953)
[39] Tulcea, C., Ionescu, T.: Mesures dans les espaces produits. Atti Accad. Naz. Lincei Rend., 7, pp. 208-211 (1949)
[40] Föllmer, H., Schied, A.: Stochastic Finance. An Introduction in Discrete Time, 4nd edition, Walter de Gruyter, New York (2016)
[41] Engelking, R.: General Topology. Heldermann, Berlin (1989) |
